San VuNgoc - Symplectic normal forms and spectral asymptotics for magnetic fields in 3D

San Vu Ngoc (1) , Fanny Bastien (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IF - Institut Fourier

I will present recent results giving precise eigenvalue asymptotics for the magnetic Laplacian for large magnetic fields (semiclassical limit), in the case of a con ning, non-uniform field, in dimension 3. The essential ingredient is the symplectic geometry of the zero-energy manifold in the magnetic phase space. Under natural conffinement assumptions for the magnetic field, one can perform three successive normal forms corresponding to three physical scales of oscillations. This is joint work with B. Hel er, Y. Kordyukov and N. Raymond.

Mots clés: Sub-riemannian day 2016; sub-riemannian; laplacian; symplectic normal forms; spectral asymptotics; magnetic fields; 3D

Mots clés: journée sous-riemannienne 2016; grenoble; laplacien; sous-riemannien

Domaines: Mathématiques [math]

San Vu Ngoc, Fanny Bastien. San VuNgoc - Symplectic normal forms and spectral asymptotics for magnetic fields in 3D : Sub-riemannian day 2016. 2016. ⟨medihal-01383705⟩